τ-curve: introduction of cusps to aesthetic curves☆ | Zendy

Kenjiro T. Miura | Zendy; Sho Suzuki | Zendy; Shin Usuki | Zendy; R. U. Gobithaasan | Zendy

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τ-curve: introduction of cusps to aesthetic curves☆

Author(s) -

Kenjiro T. Miura,

Sho Suzuki,

Shin Usuki,

R. U. Gobithaasan

Publication year - 2020

Publication title -

journal of computational design and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.764

H-Index - 24

eISSN - 2288-5048

pISSN - 2288-4300

DOI - 10.1093/jcde/qwaa014

Subject(s) - curvature , cusp (singularity) , curve fitting , torsion of a curve , osculating circle , mathematics , geometry , interpolation (computer graphics) , hessian form of an elliptic curve , tripling oriented doche–icart–kohel curve , mathematical analysis , center of curvature , elliptic curve , computer science , computer graphics (images) , statistics , animation , mean curvature , schoof's algorithm , quarter period

Yan, Schiller, Wilensky, Carr, and Schaefer pointed out that one of the demerits of clothoid interpolation is a jumping behavior during the deformation of the curve. This phenomenon occurs because the clothoid curve cannot have a cusp, where the curve is kinked or the direction of the curve is abruptly changed. We discuss how to introduce cusps for the log-aesthetic curve including the clothoid curve and propose to use for the representation of a curve the direction angle instead of curvature and define a new curve named τ-curve, which is defined by the direction angle of the curve.

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